Closed-form solutions of optimal guidance with terminal impact angle constraint

Optimal guidance laws and their closed-form solutions for controlling the impact angle as well as terminal miss are investigated in this paper. Generalized formulation of optimal guidance laws for constant speed missiles with a higher order system dynamics can be represented by a linear combination of a step and a ramp acceleration response of the missile. In the case of lag-free system, optimal guidance command is linear time varying and, therefore, the entire missile states can be expressed by polynomial functions in terms of time-to-go. We also proposed practical and precise time-to-go calculation methods in consideration of curved missile trajectory, which can be applied for various impact angle controllers. Basic properties including error analyses for the optimal guidance law for lag-free system are shown by numerical examples.